Find characteristic equation for each of the following systems. Then for each, determine if they are stable.

(a) \(\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2} \\ \dot{x}_{3}\end{array}ight]=\left[\begin{array}{rrr}-2 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & -10 & -6\end{array}ight]\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}ight]+\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}ight] u\)

\[
y=\left[\begin{array}{lll}
-1 & 3 & 3
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight]
\]

(b) \(\left[\begin{array}{l}\dot{x}_{1} \\ \dot{x}_{2} \\ \dot{x}_{3}\end{array}ight]=\left[\begin{array}{rrr}1 & -2 & 3 \\ 4 & 0 & 6 \\ -1 & 2 & 1\end{array}ight]\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}ight]+\left[\begin{array}{rr}2 & -1 \\ 0 & 0 \\ 3 & 6\end{array}ight]\left[\begin{array}{l}u_{1} \\ u_{2}\end{array}ight]\)

\[
y=\left[\begin{array}{lll}
1 & 0 & -1
\end{array}ight]\left[\begin{array}{l}
x_{1} \\
x_{2} \\
x_{3}
\end{array}ight]
\]